Advanced UV unwrap and bump map / displacement problems
I think I've done what you appear to be attempting and using of all things a moon map texture designed to be unwrapped on a sphere, certain I'd have the same problem.

I UV unwrapped it using 'Smart Unwrap' and got good results albeit with one section showing an annoying area at repeated intervals.  

Because this was aligned along the ring's circular surface , I went into the UV editor and rotated the image 90 degrees.  Then rescaled and dragged all the outer surfaces in the editor to eliminate that pattern.

The end result -